MONTPELIER — The city school board is seriously considering an operating budget increase high enough it would require a two-part vote in March. The increase — due in part to health care costs and contractual salary increases — comes as the administration and board work to minimize cuts in other areas.

“None of us want to be in this position. This is a terrible year,” said board Chairwoman Sue Aldrich. “We have awful decisions, and it’s an unusual year because there are some things that are completely out of our control that are driving costs up more than they have in the past.”

State law says districts seeking to increase spending beyond the rate of inflation plus 1 percent must break up their budget requests into two questions for voter approval, with the second representing spending above that threshold. The provision was instituted to encourage cost containment.

The board is advising the school administration not to present anything that could raise tax rates by more than 12.5 cents per $100 of assessed property value, a level of spending that would still require two budget questions on the ballot. It could add $251 to the school tax bill for a $200,000 property, bringing it to $2,873, and add $125 to the bill for a $100,000 property, raising the school portion to $1,436.

Administrators unveiled another proposal to the board Wednesday that lessened the severity of teacher and staff cuts initially proposed. Administrators will also evaluate whether two staffers in a co-curricular program not operated by the school, Community Connections, could be hired for the middle and high school to offer the same services, which range from homework clubs to mountain biking.

The strategy, developed by the school administration, would drop the overall fee the district would pay for Community Connections. Part of that savings would come from no longer paying an administrative fee to the outside program. The change would help the district reduce a Community Connections request of a $167,268 contracted expense to a $115,000 internal cost.

“It would still be able to preserve the program almost entirely as it exists,” Superintendent Brian Ricca said.

Under the proposal, the elementary school’s version of Community Connections would still be run by the existing organization.

Several people spoke against a proposed music teacher reduction. Opponents of the proposed cut included high school students involved and not involved in the music program. As of Wednesday, the administration’s proposal restored a portion of the proposed music cut, bringing back two sections of music at Union Elementary School.

Other proposed cuts reversed as of Wednesday included positions in physical education, English and English as a second language; and a counseling position for a student assistance program that involves drug and alcohol prevention efforts. None of those reversals affected full-time jobs.

Budget pressures also prompted the district to propose adding a part-time position and creating an alternative graduation program, additions that would bring revenue to the district. The working title for the service is “the SOAR Program.”

State law already provides alternative graduation opportunities to students. The process allows students to design their own curriculum and take up opportunities outside the district like with Onion River Community Access Media, said Montpelier High School Principal Adam Bunting on Friday. The program is for students who generally have difficulty with the traditional graduation route, he said.

But when students utilize the program, a school district receives less revenue based on a state aid formula tied to enrollment. Some 10 percent of Montpelier High School students did so last year, and about 7 percent will do so this year, according to Ricca. Bunting said the new program would be able to bring back significant revenue.

The administration also recommended adding a full-time co-principal at the elementary school, but the school board argued not to do so.

The district also may combine two roughly $2.3 million infrastructure bonds into a single $4.6 million bond.

The ballot question or questions on bonding would be separate from the operational budget. Some of the interest and capital payments could be part of the operating budget. The district is suggesting that a one-line operational budget is unlikely.

Major items on the first bond have included converting Union Elementary School’s steam radiators so the building could hook up to the city district heat project; a flat roof replacement at the elementary school and portions of the middle and high schools to stop costly repairs due to leaks; replacement of bleachers, which were not able to be used due to safety reasons and did not comply with the Americans with Disabilities Act; and renovations to about a third of the bathrooms in all three buildings.

Major items on the second bond have included installation of storm windows at the elementary and middle schools and an expanded parking lot at the high school.

Aldrich, the board chairwoman, said after the meeting that she feels all of the improvements are needed.

The total proposed operating budget as of Wednesday was $16.9 million, up from the current year budget of $15.7 million.